Exercice
$\frac{x^5-3x^3+4x^2-1}{x^2+1}$
Solution étape par étape
1
Diviser $x^5-3x^3+4x^2-1$ par $x^2+1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}x^{3}\phantom{-;x^n}-4x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}-3x^{3}+4x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-x^{5}\phantom{-;x^n}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{3};}-4x^{3}+4x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n;}\underline{\phantom{;}4x^{3}\phantom{-;x^n}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}+4x\phantom{;}-;x^n;}\phantom{;}4x^{2}+4x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n-;x^n;}\underline{-4x^{2}\phantom{-;x^n}-4\phantom{;}\phantom{;}}\\\phantom{;;-4x^{2}-4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}4x\phantom{;}-5\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-4x+4+\frac{4x-5}{x^2+1}$
Réponse finale au problème
$x^{3}-4x+4+\frac{4x-5}{x^2+1}$